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Problem 3 n people line up to board a plane. Each has a boarding pass with assigned seat. However, the first person has lost the boarding pass and takes a random seat uniformly. After that, each person takes the assigned seat if it is unoccupied, and one of unoccupied seats uniformly at random otherwise. Denote by Pn, the probability that the last person to board sits in the assigned seat. Show that P₁ = (P₁ + · +Pn-1), Vn ≥ 2 and use that to calculate Pn.

Problem 3 n people line up to board a plane. Each has a boarding pass with assigned seat. However, the first person has lost the boarding pass and takes a random seat uniformly. After that, each person takes the assigned seat if it is unoccupied, and one of unoccupied seats uniformly at random otherwise. Denote by Pn, the probability that the last person to board sits in the assigned seat. Show that P₁ = (P₁ + · +Pn-1), Vn ≥ 2 and use that to calculate Pn.

MATLAB: An Introduction with Applications
MATLAB: An Introduction with Applications
6th Edition
ISBN:9781119256830
Author:Amos Gilat
Publisher:Amos Gilat
Chapter1: Starting With Matlab
Section: Chapter Questions
Problem 1P
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Please do not rely too much on chatgpt, because its answer may be wrong. Please consider it carefully and give your own answer. You can borrow ideas from gpt, but please do not believe its answer.Very very grateful!Please do not rely too much on chatgpt, because its answer may be wrong. Please consider it carefully and give your own answer. You can borrow ideas from gpt, but please do not believe its answer.Very very grateful!
Problem 3 n people line up to board a plane. Each has a boarding pass with assigned seat. However, the first person has lost the boarding pass and takes a random seat uniformly. After that, each person takes the assigned seat if it is unoccupied, and one of unoccupied seats uniformly at random otherwise. Denote by P, the probability that the last person to board sits in the assigned seat. Show that P₁ = 1/2 (P₁ + ··· + Pn-1), Vn ≥ 2 and use that to calculate P₁.
Transcribed Image Text:Problem 3 n people line up to board a plane. Each has a boarding pass with assigned seat. However, the first person has lost the boarding pass and takes a random seat uniformly. After that, each person takes the assigned seat if it is unoccupied, and one of unoccupied seats uniformly at random otherwise. Denote by P, the probability that the last person to board sits in the assigned seat. Show that P₁ = 1/2 (P₁ + ··· + Pn-1), Vn ≥ 2 and use that to calculate P₁.
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